Abstract: While it was noted by R. Hardy and proved in a famous paper by C. A. Micchelli that radial basis function interpolants $s(x)=\sum\lambda_j\phi(\|x-\x_j\|)$ exist uniquely for the multiquadric radial function $\phi(r)=\sqrt{r^2+c^2}$ as soon as the (at least two) centres are pairwise distinct, the error bounds for this interpolation problem always demanded an added constant to $s$. By using Pontryagin native spaces, we obtain error bounds that no longer require this additional constant expression.

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